1. Adama Science and Technology University Chemical Engineering Program Numerical Methods for Chemical Engineers (ChE 2104 ) Errors of Numeric Result Chemical Engineering program, ASTU

2. Errors of Numeric Results Final result of computation of unknown quantities generally are approximations; that is, they are not exact but involves errors. Such an error may result from  Round off error : an error caused by chopping Chemical Engineering program, ASTU

3. Cont’d Round off rule: Discard the (k+1) th and all subsequent decimals (a)If the number discarded is less than half a unit in the k th place, leave the k th decimal unchanged. (b) If it is greater than half a unit in the k th place, add one to the k th decimal. (c) If it is exactly half a unit, round off to the nearest even decimal. Chemical Engineering program, ASTU

4. Cont’d  Example: Round off 3.45 and 3.55 to 1 decimal place Gives 3.4 and 3.6 respectively.  Experimental errors: are errors of a give data (probably arising from measurements) it is necessary to calculate errors in numerical methods (approximate computation) Chemical Engineering program, ASTU

5. Cont’d This definition doesn't account of the order of the value under examination. For example an error of a centimeter is much more significant if we are measuring a rivet rather than a bridge. Chemical Engineering program, ASTU

6. Cont’d The true value only known when we deal with functions that can be solved analytically (this is for simple systems) however real world problems in engineering are complicated we doesn’t know true answer prior. This is why we need numerical methods !!! Chemical Engineering program, ASTU

7. Cont’d Therefore, we should use an alternative methods to calculate the error. Chemical Engineering program, ASTU

8. Exercise Approximations of = 3.14159265358979… are 22/7 and 355/113. Determine the corresponding errors (true error, percent relative error) to four significant digits. Chemical Engineering program, ASTU